The series was founded in 2003. The impetus came from a project, centered around topological and algebraic methods in logic and supported by a bilateral US-Republic of Georgia grant, with the purpose of forging collaborations between the group of Leo Esakia in Tbilisi and the group in Las Cruces NM initiated by Mai Gehrke. The participants in Georgia were Leo Esakia (PI), Revaz Grigolia, Mamuka Jibladze, Dito Pataraia (participants), and Nick Bezhanishvili and David Gabelaia (students). The participants in the US were Mai Gehrke (PI), Guram Bezhanishvili, John Harding, and Patrick Morandi (participants), with Guram Bezhanishvili, who had been recruited a few years prior in NM, as major contributor to this project linking his group of origine and his new home.
The first meeting was held in Tbilisi, under the name International Conference on Algebraic and Topological Methods in Non-Classical Logics. In 2005, a second installment expanded the theme, paying particular attention to multivalued logics and residuated structures. This meeting took place in Barcelona, organized by the research group around Josep Maria Font and Ramon Jansana. In 2007, the third meeting was held in Oxford, organized by Mai Gehrke and Hilary Priestley. There were also satellite workshops organized by Bob Coecke, Alexander Kurz and Michael Zacharyaschev. By 2007, a cohesive community, much bigger than the original founding members, had emerged. It involved researchers from many different fields including lattices and Stone duality, modal and intuitionistic logic, universal algebra, and categorical methods in logic and computer science. And the conference series was successfully fostering meaningful interactions between these fields that had previously evolved separately. Although category theory had been a topic of the conferences since the beginning, it was agreed, at the Oxford meeting in 2007, that it should be made clearer by changing the name to Topology, Algebra, and Categories in Logic.
Also in 2007, a steering committee was formed. The purpose was to ensure the long term goals of the series while allowing the individual program committees and meetings to have a stronger emphasis on one or two of the fields feeding the TACL community.
The current members of the Steering Committee are:
The biannual series continues to make strong links between fields, mainly general or pointfree topology, universal algebra and lattice theory, and category theory by focussing on shared applications in logic. It also brings researchers together from many parts of the world: Eastern and Western Europe, Africa, the Americas and the Far East, including Japan, Australia, and New Zealand. As the majority of participants come from Eastern and Western Europe, most of the conferences of the series have been held in Europe. As a consequence, a US-based sister series under the name Boolean algebras; Lattices, algebraic logic and quantum logic; universal Algebra, Set theory; and set-theoretic and point-free Topology (BLAST), was formed in 2008 and is held annually in the mountain/western/midwest region of the USA.
Based on a request from the participants of the TACL series, an associated summer school has been added since 2013. The purpose of the school is to prepare and initiate young researchers and newcomers to the interdisciplinary research featured at TACL and to foster and strengthen the sense of community among the young members of the community. The program is usually focused around 4 courses with at least one from each of topology, algebra, and categories as applied in logic. Lecturers are chosen for their leadership in research but also for their excellence in communication. An effort is made to have adequate funding available in order for potential participants with few financial means to be able to participate.